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Zbl 1167.26303
Gorenflo, Rudolf; Mainardi, Francesco
Fractional relaxation of distributed order.
(English)
[A] Novak, Miroslav M., Complexus mundi. Emergent patterns in nature. Hackensack, NJ: World Scientific. 33-42 (2006). ISBN 981-256-666-X/hbk

A detailed study of the distributed order fractional relaxation equation $$\int^1_0 b(\beta) u^{(\beta)}(t)\,d\beta= -\lambda u(t) +q(t), \quad t\ge 0,\ \lambda > 0$$ subject to the initial condition $u(0^+) = c_0$, where $b(\beta) \ge 0$, and $\int^1_0 b(\beta)\,d\beta =1$ is carried out. In particular, the structure of its solution and in a few cases their asymptotic behaviour near zero and near infinity are also investigated.
MSC 2000:
*26A33 Fractional derivatives and integrals (real functions)
44A10 Laplace transform
45J05 Integro-ordinary differential equations

Keywords: distributed order fractional relaxation equation; Laplace transform; homogeneous equation

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